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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 131118o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 131118.e4 | 131118o1 | \([1, 0, 1, -32815, 47763746]\) | \(-822656953/207028224\) | \(-983405644829097984\) | \([2]\) | \(2662400\) | \(2.1317\) | \(\Gamma_0(N)\)-optimal |
| 131118.e3 | 131118o2 | \([1, 0, 1, -2184495, 1231187746]\) | \(242702053576633/2554695936\) | \(12135072000059064576\) | \([2, 2]\) | \(5324800\) | \(2.4783\) | |
| 131118.e1 | 131118o3 | \([1, 0, 1, -34863135, 79228565698]\) | \(986551739719628473/111045168\) | \(527476123459357488\) | \([2]\) | \(10649600\) | \(2.8249\) | |
| 131118.e2 | 131118o4 | \([1, 0, 1, -3932735, -1018447486]\) | \(1416134368422073/725251155408\) | \(3445018589093690885328\) | \([2]\) | \(10649600\) | \(2.8249\) |
Rank
sage: E.rank()
The elliptic curves in class 131118o have rank \(0\).
Complex multiplication
The elliptic curves in class 131118o do not have complex multiplication.Modular form 131118.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
